96-451 Giuseppe Dito and Moshe Flato

Generalized Abelian Deformations: Application to Nambu Mechanics (54K, LaTeX with AMS-Fonts) Sep 30, 96

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Abstract. We study Abelian generalized deformations of the usual product of polynomials introduced in mp_arc/96-39. We construct an explicit example for the case of $\frak{su}(2)$ which provides a tentative of a quantum-mechanical description of Nambu Mechanics on ${\Bbb R}^3$. By introducing the notions of strong and weak triviality of generalized deformations, we show that the Zariski product is never trivial in either sense, while the example constructed here in a quantum-mechanical context is only strongly non-trivial.

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